The polarization of photons produced in radiative B_{s}^{0} decays is studied for the first time. The data are recorded by the LHCb experiment in pp collisions corresponding to an integrated luminosity of 3 fb^{-1} at center-of-mass energies of 7 and 8 TeV. A time-dependent analysis of the B_{s}^{0}→ϕγ decay rate is conducted to determine the parameter A^{Δ}, which is related to the ratio of right- over left-handed photon polarization amplitudes in b→sγ transitions. A value of A^{Δ}=-0.98_{-0.52}^{+0.46}_{-0.20}^{+0.23} is measured. This result is consistent with the standard model prediction within 2 standard deviations.